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By Alan Arias

On grinding in pure water, zirconium, tantalum, iron, and stainless-steel powders were extensively comminuted and simultaneously oxidized with hydrogen release, whereas nickel, copper, and silver powders did not react with water and their particle sizes increased. On grinding nickel, copper, and silver in water pressurized with oxygen, nickel and copper became extensively comminuted and were oxidized, whereas silver did not react with oxygen and its particle size increased. From these results and other considerations , it is hypothesized that for extensive comminution of ductile metals and alloys to occur on grinding they must react with the grinding media. UlTRAFINE metal and alloy powders are finding an ever-growing number of applications in metallurgy and in other fields.' Of particular interest are ultrafine metal and alloy powders suitable for dispersion strengthening.2'9 Various research programs on dispersion strengthening are being carried out and in some of these programs the ball-milling method is being used to produce dispersion-strengthened materials. This method usually involves the simultaneous grinding of metal or alloy and a dispersoid followed by consolidation of the resulting powder mixture. To obtain the ultrafine powders required for dispersion strengthening,' grinding is carried out in many liquids, including aqueous and nonaqueous media, with or without grinding aids.4'5 Nonaqueous liquids usually contain water as an impurity and some grinding aids may contain water of hydration.5 The water present may affect the grinding process. The writer has shown5 that. on ball milling chromium in water, the chromium is oxidized and hydrogen is released. It was surmised that the same reaction may occur on ball milling other metals and alloys in waterbearing liquids. Therefore, the investigation of ball milling in water was extended to metals and alloys other than chromium. In the course of the investigation, however, it became apparent that the data-to-gether with the results from a few additional experi-ments—could be used to postulate a comminution mechanism for ductile metals and alloys. A well-known comminution theory is that of smekal.7 According to this theory, comminution is possible because of the weakening effects of surface cracks and other imperfections in materials. This theory imposes a lower limit of about 1 µm for the ground particles. The beneficial effects of liquids and additives on the rate of grinding are well known.8 Mechanisms by which liquids and additives may aid in grinding were reviewed by Rose and Sullivan.' One aspect of these effects is based on Rehbinder's theory of crack propagation in materials under stress.9 According to Reh-binder's theory, liquids or additives may promote the spread of cracks in stressed materials by lowering the surface tension at the crack tip. Rose and Sullivan surmise that the same mechanism may be operative during grinding, thereby facilitating comminution of the particles. In addition, Rose and Sullivan reviewed how additives may act as dispersants as a result of their being adsorbed on the surface of the particles being ground. This concept has been suggested by Quatinetz, Schafer, and smea15 to explain from their experiments the major role of additives that enabled them to grind metal down to 0.1 µm. Discussions of other comminution theories and additional sources of material on the subject will be found in Ref. 10. None of these previous suggestions and theories, however, can account for all phenomena encountered during ball milling of metals to submicron size in this and in a previous investigation by the author.6 The objectives of this investigation were to determine the behavior of metal powders during ball milling either in pure water or in oxygenated water and to gain an insight into the grinding mechanism. Zirconium, tantalum, iron, nickel, copper, and silver powders were ball-milled in pure water. These metals were selected because their oxides cover a wide range of free energies of formation. For comparison purposes, an alloy-type 430 stainless steel-was also ball-milled in pure water. The pressure of the hydrogen released during ball milling was monitored in order to determine the oxygen that combined with the metal or alloy. In order to obtain more information on the nature of the grinding process, nickel, copper, and silver powders were also ball-milled in oxygenated water (water pressurized with oxygen). The oxygen that reacted with the powders was determined from the pressure decrease in the mills. The powders resulting from ball milling in pure water and in oxygenated water were subjected to surface area, optical microscopy, and X-ray diffraction analyses. With these data, the oxygen calculated to be combined with the metals during ball milling, and comparison of the free energies of formation of the oxides of the milled powders with that of water, a comminution mechanism was postulated. MATERIALS, EQUIPMENT, AND PROCEDURES The materials used in this investigation were powdered metals, deaerated distilled water, high-purity helium, and commercial grade (99.5 pct purity) oxygen. The powdered metals used were zirconium, tantalum, iron, nickel, copper, and silver. A 16 pct Cr, ferritic stainless steel, type 430, was also used. The purities (or nominal compositions) and the surface areas of these metals and the alloy are given in Table I.

Jan 1, 1970

By J. Szekely, G. P. Martins

A formulation is given for describing the rate of expansion of spherical bubbles rising in liquids the freeboard of which is evacuated. The computer solution of the resultant differential equations has shown that, for low freeboard pressures (less than about 5 mm Hg), on approaching the free surface the bubbles expand much less rapidly than predictable from equilibrium considerations. In other words, in this region the pressure inside the bubbles will be significantly larger than the static pressure in the liquid corresponding to the position of the bubble. These theoretical predictions were confirmed by experimental work, using two-dimensional air bubbles rising in mercury. The important consequence of these findings is that the expansion of gas bubbles in vacuum degassing operations will be a great deal less than expected from hydrostatic considerations. This would lead to a significant reduction in the available interfacial area and may explain the apparent poor efficiency of many vacuum degassing units. VACUUM degassing as a treatment for liquid steel has gained widespread popularity in recent years; the number of known installations exceeds several hundred at the present time.' Although much information is available on both the thermodynamics of the system and the overall performance of various industrial units, much less is known about the fundamental aspects of the process kinetics.2-4 The basic physical situation common to virtually all vacuum degassing operations is the interaction between gas bubbles (swarms of bubbles) and the surrounding molten metal, held in a container, the freeborad of which is at a low absolute pressure. Once formed (or introduced from an external source) the bubbles will ascend, due to the buoyancy forces, and, during this ascent, a significant increase in their volume will occur. This progressive increase in the bubble volume is due to two factors: a) the continuous reduction in the static pressure acting on the bubble during its rise; and b) mass transfer into the bubble from the surrounding molten steel. In a recent paper Richardson and Bradshaw developed equations5 for describing mass transfer into gas bubbles from molten metals at reduced pressures. However, in deriving these expressions it was assumed that the pressure inside the bubble was identical to the static pressure in the adjacent liquid. In other words, the volume of the bubble was considered to be in equilibrium with the pressure of the fluid adjacent to it. This assumption, thus their analysis presented, was thought to be reasonably accurate for most of the bubble's ascent; however, it was unlikely to be valid in the immediate vicinity of the free surface, held at a low pressure. It was pointed out in the discussion6 that the region close to the surface may be of considerable importance as both the driving force and the interfacial area available for mass transfer are at their highest value here. The ' 'anomalous" behavior of gas bubbles when approaching a free surface at low pressures was recently confirmed in a preliminary investigation by Szekely and Martins. ?1 Here high-speed motion photography was used to study air bubbles rising in a column of n-tetradecane with a freeboard pressure of 0.1 mm Hg. It was found that significant distortion of the bubbles occurred on approaching the free surface; furthermore, the expansion observed was much less than what one could expect from hydrostatic considerations, i.e., factor a previously discussed. It follows from the foregoing that a detailed study of these phenomena would be justified both from fundamental considerations and because of their potential relevance to technology. The purpose of the paper is to present a more realistic formulation for the expansion of a gas bubble approaching a low-pressure region, together with a comparison of the theoretical prediction with experimental measurement. An inert bubble will be considered in the first instance; it is thought that the understanding of the fluid mechanics is an essential first step toward the realistic formulation of the mass transfer process. This latter problem will be the subject of a subsequent publication. FORMULATION The Physical Model. Consider a spherical bubble, of initial radius Ro, rising in a fluid, having a density pL. Initially let the bubble be at a distance H from the free surface, and at a pressure Pgo, as illustrated in Fig. 1. Pgo, the initial pressure in the bubble, is given by the following equation: pgo = Po = Ptp +pLgH [ la] where Po is the pressure in the liquid corresponding to the initial position of the bubble and Ptp is the pressure at the free surface. The fluid pressure at

Jan 1, 1970

By W. F. Chiao

With the application of dislocation damping theory an attempt was made to determine whether the generation and extension of dislocations is inherently more difficult in a brittle steel than in a ductile steel. A ductile steel was compared with a brittle stee1 by simultaneously measuring the ultrasonic attenuation and velocity during tensile test, and the density of free dislocations and their mean loop length were then calculated as a function of strain. The results showed that in the ductile steel there was always a large generation of dislocations and great extension of loop length occurring at some stage within the early plastic region. In contrast, the brittle steel showed very little or no such sudden changes in dislocation dynamic states after the onset of plastic deformation. Furthermore, a strong temperature dependence of dislocation dynamic states was also observed in the ductile steel and a hypothesis was suggested that a thermally activated process of dislocation rearrangement could occur at higher deformation temperatures. The activation energy of dislocation rearrangement at room temperature was estimated as about 2030 cal per mole.C. DUCTILITY is an indispensible property in the application of engineering materials, especially steel. During the past two decades the theoretical and experimental approach to the understanding of flow and fracture of metals has been constantly undergoing changes and progress." while the fracture behavior of metals can be influenced by many factors such as chemical Composition,3 second-phase particle mor-phology,4 and dislocation arrangement,5 it is now a general belief that the fundamental understanding of the ductile-brittle fracture phenomena of solid materials must stem from the study of dislocation dv-namics developed under stress conditions.6,7 Most of the traditional ductility tests, such as Charpy impact test, slow bend test, and tensile fracture test, cannot by themselves reveal directly the mechanisms of ductile to brittle transition of materials. In the experimental investigation of tensile ductility it would be ideal to be able to study directly the dynamics of dis-locations in a bulk specimen during the process of deformation. Since the ultrasonic pulse technique is the only satisfactory method for studying dislocations and the fine details of deformation characteristics in metals in the course of a tensile test, it would appear that a comparative study of ultrasonic attenuation changes during tensile tests of metallic materials exhibiting different ductility might be very informative. So far no work comparable to this study has appeared in the literature. Recent progress in both theory and experiment has indicated the feasibility of studying the dislocation mechanisms of ductility behaviors by ultrasonic measurements during tensile test. Granato and Lucke8 have developed a quantitative theory that enables the calculation of dislocation density and their average loop length from the measurements of ultrasonic attenuation and velocity, and several investigators, including Chiao and Gordon,9'10 have shown that simultaneous ultrasonic measurements can be successfully made during a tensile test. Furthermore, many investigators11-13 have repeatedly proposed in the past several decades that deformation and fracture are mutually self-exclusive, and that the ability or inability of a material to deform plastically, i.e., to generate dislocations, is a major factor in determining whether the material will be ductile or brittle. Thus, in the present work an attempt was made to determine whether the generation and extension of dislocations is inherently more difficult in a brittle steel than in a ductile steel. This article is principally concerned with the study of the relation between the propagation of ultrasonic waves and tensile deformation in a steel series which displays quite different toughness at room tempera-turk. changes in attenuation and velocity of ultrasonic waves have been measured as a function of strain during the deformation process. The results have been interpreted in terms of the vibrating string model for dislocation damping as developed by Granato and Lucke, and it has been found that some of the more subtle predications of the model are in good agreement with the experiments. This would be especially meaningful because most of the previous experiments in testfying the model were carried out with single crystals of high-purity materials and little work has been done with polycrystalline steel alloys. EXPERIMENTAL PROCEDURES AND RESULTS Specimen Materials. The tensile specimens used throughout this experiment were of two compositions selected from a series of Fe-Mo-0.77 pct Mn-0.22 pct C steels prepared for a ductile-brittle fracture transition study. One steel contains 0.21 pct Mo and the other 1.03 pct Mo. These two compositions were chosen for the present study because they possess quite different toughness properties at room temperature. The 0.21 pct Mo steel is quite ductile while the 1.03 pct Mo steel is rather brittle, as measured by the standard Charpy impact test. The alloys had been prepared by vacuum induction melting and chill casting in steel molds. The ingots were hammer-forged into 1/2-in.-sq bars from which tensile specimen blanks were cut. These blanks were first normalized under argon atmosphere at 1700°F and then reaus-tenitized and isothermally transformed at 1050°F to a bainitic microstructure. The chemical compositions, heat treatments, hardness measurements, and Charpy transition temperatures of the two steels are listed in Table I.

Jan 1, 1970

By H. E. Exner

This article is a critical review of the influence of surface preparation on crack formation at Vickers indentations in the test used by Palmqvist3-7 to evaluate the toughness of cemented carbides. Experimental results are presented which clearly show that grinding introduces compressive surface stresses into the cobalt phase and thus reduces the crack length. The deformed surface layer is removed by polishing and a stress pattern is approached corresponding to that in the bulk material. Cracks of maximum length are characteristic of this stress state. Deformation stresses can be removed by annealing above 800°C. On the basis of these results , sample preparation for the crack length test can be simplified, the accuracy of measurement is improved, and a simple and significani parameter is found to describe crack resistance of cemented carbides. FOLLOWING suggestions by Ammann and Hinniiber,1'2 Palmqvist3-7 developed a method for testing the toughness of cemented carbides using as a measure the sum of crack lengths at the four corners of a Vickers hardness indentation. This method has several advantages over the bend test commonly used in carbide technology: a) specially formed samples are unnecessary; b) sufficient information can be obtained from one sample; c) the scatter is relatively small; d) the range of actual values for commercial cutting alloys is wide. Thus, this test is both cheaper and more precise than the bend test. Nevertheless, Palmqvist's method is not widely used, mainly for two reasons: a) The relationship between crack length and the technological properties of the material (wear and shock resistance) is not clear. b) The crack length is strongly dependent on surface treatment. It is necessary, therefore, that surface preparation be very precise and reproducible, conditions usually hard to obtain. While any other simple mechanical test has this first drawback, the second became crucial in the application of the crack length method as a practical test. The reasons that this drawback could not be eliminated are, in our opinion, misleading and inconsistent interpretations of the influence of surface preparation on the crack length given in literature. In the following, after a short review of previous experimental results the interpretations given by different authors,4?'-11 cf. Table I, are discussed critically and a consistent explanation is presented on the basis of which improvements of the method of crack length testing are proposed. 1) PREVIOUS EXPERIMENTAL RESULTS In his first attempt to use the cracks at Vickers impressions as a quantitative measure of the toughness of cemented carbides, palmqvist3 calculated the work necessary to initiate cracks by the formula: Sk =k.Pk. [I] where k = numerical constant = 6.49, Sk = critical work to initiate cracks (gf cm), Pk = critical load (load necessary to initiate cracks) HV = Vickers hardness (kp per sq mm). The difficulties involved in experimental determination of the critical load were overcome by the observation that a linear relation holds between the applied load and the sum of the crack lengths at the four corners of the indentation. This linear function, given by Eq. [2] below, was confirmed by Dawihl and Alt-meyer9and by our experiments, see Fig. 1: I = a1.P +a2 [2] where 1 = sum of the crack lengths at a Vickers indentation, P = applied load, al, a2 = parameters dependent on the toughness of the alloy and the surface preparation. The critical load, Pk, is now given by a2, which can be obtained by extrapolating the load vs crack length line to zero crack length, see Fig. 1. This simple relationship, Eq. [2], led Palmqvist1,7 to a parameter which was more reproducible and easier to obtain experimentally than the critical work: the work, S300, put into the sample to produce an average crack length of 300 µm per indentation. This parameter is calculated using the formula: where the load, P3oo, giving a crack length of 300 µm, can be taken from the load-crack length plot, Fig. 1,

Jan 1, 1970

By G. S. Cole, G. F. Bolling

A series of Al-Cu alloys has been cast from constant superheat to solidify either with a hot top or with a free liquid/air interface. All the other variables which affect relative fluid motions were kept constant except the imposition of slow rotations m oscillations of the mold. Depending upon the exact circumstances, evi-dence could be found for the nucleation of equiaxed grains from dendrite bits detached from the columnar zone, or from the free surface, or from solid bits induced at pouring; a special experiment showed the solute buildup during ingot solidification and by inference the reality of constitutional supercooling. All methods of grain nucleation are thus supported. When solidification is arranged in a static mold the columnar- to-equiaxed transition occurs by one of these nucleation paths, subject to the natural decay of temperature gradients which promotes nucleation or the survival of nuclei. But when solidification is forced under special fluid flows it may display odd transitions. In one of these the equiaxed zone is synihesized from. dendrite bits detached from the solid/liquid interface. These survive under the concurrent lowering of temperature gradients and eventually cause transition by impeding columnar growth. GRAIN structure control is desired because real experience shows that specific properties are associated with specific cast grain structures. But since control is thus a matter of need and does not require understanding, much of casting remains art. For example, the manipulation of relative fluid motions in simple ingots provides a control of grain structure development,1-4 but theoretical insight is not required in order to broaden its potential applicability. Fortunately, however, once a variable like fluid flow is recognized it can also provide paths toward new insight. New observations using this variable have provided an insight which is curious. All the theories or descriptions of the columnar-to-equiaxed transition (CET) seem to be supported as long as the appropriate experiment is carried out. In order to develop this idea, let us ignore segregation, the chill zone (until a later section of this paper), and the origin and development of the columnar zone.= The details of questioning how equiaxed material forms in a casting may be divided in two. The first part is simply a questioning of the origin for equi-axed grains: are there fresh nuclei from heterogeneous nucleation, or dendrite bits broken off or melted from the columnar zone or elsewhere,6 or other solid bits surviving from the outset of freezing? The second is more complex, a questioning of the CET: does columnar growth slow down and allow the dominance of equiaxed grains, however they are formed, or do equi-axed grains take over and force columnar growth to stop? This "chicken-or-the-egg" second question can be quite useful, especially because it allows us to delineate the ordinary or NATURAL EQUIAXED ZONE and the induced or SYNTHETIC EQUIAXED ZONE. A natural equiaxed zone occurs if solidification proceeds in the absence of disturbances or extraneous forces such as ultrasonics, stirrings, and so forth. Both the CET theory proposed by Winegard and Chal-mers, 7requiring constitutional supercooling, and the CET theory suggested by Chalmers,8 requiring nuclea-tion only on pouring, pertain to the natural equiaxed zone. The best collating evidence to date for both these theories is contained in the work by Biloni and Chal-mers;9,10 the former theory7 is supported by special versions of the unidirectional growth experiment performed by Plaskett and winegardl1 and the latter theory' is supported in detail for the solidification of small ingots. An equiaxed zone can be synthesized when disturbances caused by forced fluid flows2-4 or other artificial means9,10 break off or melt off dendrite tips from an advancing solid/liquid interface,* if (and only if) temperature gradients in the melt are (forcibly) reduced enough to ensure the survival of these bits of dendrites, 2'3 Willful disturbances even so trivial as those produced by rapping a mold might be included here; as will be shown for example, this follows Southin's suggestion that the free liquid/air interface

Jan 1, 1970

By Richard H. Siller, Rex B. McLellan

A model for interstitial solid solutions has been considered in which a repulsive Potential exists between interstitial atoms in the solvent lattice. It has been shown that this model is consistent with the thermodynamic Properties of certain interstitial solid solutions. The model is then applied to the calculation of the variation of the diffusivity of carbon in au-tenite with composition. Although the energy levels at the saddle point, and thus the absolute values of dif-fusivity, cannot be calculated, it is shown that by taking the repulsive interactions between the diffusing atoms into account the functional form of the dependence of diffusivity on solute concentration can be derived. ThE composition dependence of the diffusivity, D, of carbon in austenite at a given temperature is well-known.'-3 smith3 tried to reconcile the observed composition dependence of D at 1000°C with the previously observed4 composition dependence of carbon activity using equations for D derived by arken5 and Fisher, Hollomon, and Turnbull,6 but was unsuccessful. In this paper we shall modify the approach of Fisher et al. by considering the "blocking" model7 for interstitial solid solutions, based on concept due to Speiser and Spretnak,' in which a repulsive potential exists between interstitial solute atoms in the solvent lattice, causing a certain number of interstitial sites to be "blocked" from occupancy by further solute atoms. We shall thus be able to describe the intimate relationship between the composition dependence of carbon diffusivity, a kinetic phenomenon, and the composition dependence of carbon activity in austenite. THEORY Consider for convenience one-dimensional interstitial diffusion in an fcc lattice in the [loo] direction. Fig. 1. Assume that solute atoms occupy octahedral sites only.7,9'10 These octahedral sites are located on {lOO} planes a/2Å apart. A solute atom, A, occupying an octahedral site on a {100 } plane denoted by 2, has twelve nearest-neighbor octahedral sites: four on plane 1, four on plane 2, and four on plane 3. Diffusion occurs when there is a net flux of solute atoms, through an imaginary plane shown with dashed lines, from plane 2 to plane 3. Fisher et al6. use the concept of activated complexes, as given in the theory of absolute reaction rates." They show that the number of solute atoms per cubic centimeter per second which pc — Fig. 1-Diagram showing the arrangement of octahedral sites (x) in the fcc lattice. pass in the direction of diffusion from activated to new interstitial position is: ?where C is the concentration of the solute in atoms per cubic centimeter, l/m + is the fraction of new interstitial positions corresponding to motion in the forward diffusion direction (transmission coefficient), ?F* is the free-energy difference between the activated complex and the reactants when each is in its standard state at the temperature of the reaction (independent of temperature and composition in the case of carbon in austenite), y is the activity coefficient of the solute species, and, finally, ym is the activity coefficient of the activated complex (assumed constant). The flux of atoms moving in the forward direction through an area of 1 sq cm perpendicular to the direction of diffusion is therefore: m+ Ym l ' atoms per second where is the distance between planes. The blocking model states that a nearest-neighbor octahedral site of a given solute atom has a probability, f, of being inaccessible to other solute atoms. The number of available sites for diffusion on a given plane will, therefore, depend on f, which is constant, and Nu, the number of solute atoms on that plane. The effect is to have more available sites in the diffusion direction, thereby increasing the net flux of solute atoms. This is reflected in the transmission coefficient, l/m. To calculate the transmission coefficient for solute

Jan 1, 1970

By G. W. Toop

In a recent publication,31 Darken has derived an equation to describe thermodynamic behavior in ternary metallic solutions with compositions near pure component 1: Eq. [I] is understood to be a general equation, consistent with the ternary Gibbs-Duhem equation, which is proposed as a logical formalism in view of observed behavior in some binary metallic solutions31'32 rich In Eq. and am are constants obtainable from the 1-2 and 1-3 binaries. The parameter 023 may be determined from measurements on the ternary The purpose of this discussion is to compare Eq. [I) or [3] with other ternary formulations involving binary terms, within the regions of validity of Eqs. [I], [2], and [3]. First, the ternary point is considered to be at the intersection of two composition paths, one with constant N1 and another with constant N2/N3 as shown in Fig. 10. The terms in Eq. [3] may be related to the binary points shown by multiplying the first term on the right-hand side of Eq. [3] by N2 (1) /l -N1, the second term by the third term by and the fourth term by each multiplier being unity: It should be noted here that no suggestion has been made that either the binary or the ternary systems form regular solutions. However, Eq. [5] and hence Eq. [3] shows that the contribution made to the ternary excess free energy from the 1-2 and 1-3 binaries has the same form as for a regular ternary system.1 Before considering the term a23 for the above case, a second geometrical relationship is examined with the ternary point at the intersect ion of three composition paths with constant N1/N2, N2/N3, and Nl/N3, respectively, as shown in Fig. 11. For this geometry, ternary values of NZ and N3 in terms of the binary values shown may be substituted into Eq. [I]. Then by making use of identities of the form Eq. [6] contains terms that are similar to those in a ternary regular solution formulation34 based on the geometry shown in Fig. 11. Although at finite concentrations, unless the 1-2 and 1-3 binaries form

Jan 1, 1968

By W. F. Flanagan, K. R. Evans

The strong temperature dependence of the flow stress of bcc metals has prompted considerable interest and controversy concerning the rate-controlling influence of the Peierls' mechanism upon deformation in metals.18"21 Dorn and Rajnak" recently offered a criterion for Peierls' deformation utilizing a line-energy model of a dislocation to estimate the saddle-point activation energy, for the nucleation of a pair of kinks as a function of applied stress and the height and shape of the peierls9- barrier. It was found that Un/2Uk, where 2Uk is the excess energy of a kink pair, was a unique function of where is the effective stress and 7p is the Peierls' stress as defined in Fig. 20. The relationship found by Dorn and Rajnak between is given by the solid line of Fig. 21. may be expressed in terms of the temperature of test, T, and the athermal temperature, T,, defined in Fig. 20. Considering the strain-rate, 9, of deformation for a thermally activated process to be given by where fo is nearly a constant, it is seen that and the theoretical relationship of Fig. 21 may be examined with readily obtainable experimental parameters. Dorn and Coworkers analyzed a large amount of experimental data in this manner for materials sus-

Jan 1, 1967

By J. V. Gluck

In the present paper," as in earlier publications, V1'2"1 the authors present experimentally obtained relations for the free energy of solution of oxygen in various metals as a function of temperature. The relations are linear and given in slope-intercept form. The authors give values for the "probable error" of the slope and intercept, citing Birge's method17 for obtaining these quantities. Birge discussed these methods as early as the period 1929-32.25726 In Ref. 25 the probable error is defined as "the numerical value which the true error is as likely to exceed as not", i.e., 50 pct probability. Ref. 26 is even more detailed and includes a lengthy discussion of the applicability of the Gaussian distribution to experimental data. However, the use of the "probable error" has come under some question. For example, Ezekiel'~ states that "the use of the probable error tends to make the results appear rather more accurate than the standard error". Moroney28 stated (in 1951) that "the term 'probable error' was used in former times to denote 0.67450 (50 pct confidence using the normal distribution)....the term, a poor one, is now very much obsolescent. It has been said that 'it is neither an error nor probable' ". Bennett and Franklin in 1954" in discussing statistical confidence levels mentioned that "the customary use of the 5 and 1 pct levels is not completely a matter of chance; these levels probably represent a balance between the desire to be correct and the desire to be specific. Also in most people's minds the borderline between something that could possibly happen and something that is not likely to happen is somewhere in this region. Certainly 5 or 1 pct confidence limits are to be preferred to limits such as the 'probable error' which has only a 50/50 chance of including the correct value." It may readily be seen that the 95 pct confidence level, which is given by 1.960 (assuming large sample size), thus corresponds to approximately three times the "probable error". Indeed, limits of one standard deviation correspond only to about 68 pct probability. Even if we triple the tolerances given by the authors in the equations of their Table 111, the deviations do not become excessive and would not detract from their excellent results. It could then be said with a high degree of confidence (95%) that the precision of the slope and intercept values is about *3-5 percent of their absolute levels rather than the 1-2 percent implied in Table 111. This is then compatible with an earlier suggestion of Gokcen~' of a probable accuracy of 5 pct in dissolved oxygen measurements by the technique employed. Alternatively, the authors could have

Jan 1, 1967

By John Chipman

The concentration of a solute in a dilute ),zetallic solution may be measured by any of several parame- ters including weight percent, atom fraction, atom ratio, and lattice ratio. The ratio of filled to unfilled interstitial sites is useful for interstitial solutes. A variable 2 proportional to this ratio is used as a measuve of concentration. For component 2 irz a bitzary solution z2 = n2/Ym - nz/b) where b is the numberber of interstitial sites per lattice atom. For a t~lul-ticortzporzent solution this becomes zz = n2/(nl + Cvjnj) in which Vj = - l/b for an interstial solute and +1 for a substitulional solute. In the infinitely dilute solution the activity of an interstitial solute 2 is proportional lo z2. At finile concentration the departure from this limiting law is expressed us an activity coefficient, his coefficient is a function of concentra1io)z expressed as tevactiolz coeffcient 8; is analogous to the jark~iliar e£ bul is found to be independent of concentvation in certain solutions for which data are available. It is found that the same equations may be used to express the activity of a nonmetallic solute, sulfur, in liquid solutions of iron containing other solutes, both metallic and nonmetallic. For a nonmetallic solute or for one which strongly increases the actiuity of sulfur, it is convenient to assign arbitvarily a value vj = — 1. When this is done the derivative is found to be constant in each of the ternary solutions studied. The activity coefficient of sulfur in a complex liquid iron solution may be expressed as where nk is a second-order cross product determined in the quaternary solution Fe-S-j-k. The equation is used to calculate tlze activity of sulfur i)z three sevetl- component solutions. IN thermodynamic calculations concerning dilute solutions it is unnecessary to invoke laws and relations which extend across the concentration range to include concentrated solutions. In most binary metallic systems, as arkeen&apos; has recently pointed out, there exist two terminal composition regions of relatively simple behavior, connected by a central region of much greater complexity. When the solute is a nonmetal there is only one such region and in many systems the concentration range is extremely limited. It is the purpose of this paper to suggest a method for the calculation of activities in such a terminal region in which one or more solutes are dissolved in a single solvent of predominantly high concentration. HENRY&apos;S LAW In the usual textbook statement of Henry&apos;s law, concentration is stated in mole fraction. This has the advantage that it makes Henry&apos;s law thermodynamically consistent with Raoult&apos;s law. Since all measures of concentration at infinite dilution are related by simple proportion it follows that mole fraction, molality, atom ratio, weight percent, or any other unit of concentration can be used with the appropriate constant. At finite concentrations, however, calculations based on the law depend upon the unit employed. Deviations from Henry&apos;s law at finite concentrations depend upon the composition variable employed. They are evaluated in terms of activity and interaction coefficients2 which have become familiar features of metallurgical thermodynamics. It is the purpose of this paper to propose a measure of concentration for metallic solutions containing interstitial or nonmetallic solutes by means of which the calculation of activities in complex solutions may be simplified. The discussion will be restricted to free-energy interaction coefficients3 typified by Wagner&apos;s c|a BINARY SOLUTIONS The several measures of concentration which are to be considered are shown in line a of Table I. The corresponding activity coefficients are in line b and the deviation coefficients, sometimes called self-interaction coefficients, are in line c. Henry&apos;s law simply states that the activity coefficient approaches a constant value at infinite dilution. By adoptihg the infinitely dilute solution as the reference state and defining the "Henrian" activity as equal to the concentration in this state, the activity coefficient is always unity at infinite dilution. This convention is far sim~ler and more useful in dilute solution than emploiment of the &apos;Raoultian" activities and it will be used in the following discussion. The several definitions and equations of Table I will be referred to by means of their coordinates in the table. Early observations of deviations from Henry&apos;s law in metallic solutions were shown graphically4 rather than analytically. For the case of sulfur in liquid iron5 the slope of a plot of logfs vs (%S) was constant in the range 0 to 4.8 pct S, indicating constancy of eh2&apos; in Ic. He was proposed by wagnerz and has been widely adopted. The a function of IIIc recently employed by ~arkenl was designed specifically for dilute solutions. Darken has shown that the value of a12 remains essentially constant for many binary solutions within a substantial range of compositions. The atom ratio is directly proportional to the molalitv.<, a conventional measure of concentration. IVb and C served as the basis for smith&apos;s6 classic studies of

Jan 1, 1968

By Klaus Schwerdtfeger

In order to test the performance of ZrO, (CaO) and Tho,(Yz03) electrolytes in the electrochemical determination of oxygen activities in liquid metals at steel-rrzakitng temperatures , electromotive force measurements have been made with the following cells: The oxygen-- activities are calculated from the electmrnotive forces for the investigated systems. The standard free energy of- formation of MnO and the activity of manganese in Fe-Mn melts are derived. Indications are that the Zr 0z(Ca0) electrolyte exhibits little electronic conductivity at oxygen pressures as low as 10&apos;a atnz at 1600°C; however, the partial electronic conductivity may become noticeable at lower oxygen activities. The Tho,(Yz03) electrolyte is found to be an ionic conductor at the oxygen pressure as low as that for the Mn + MnO equilibrium, but exhibits partial electronic conductivity at oxygen pressures higher than 10"1 atm (1500°C). fi. better control of oxidation and deoxidation reactions in steelmaking may be facilitated if the oxygen activity in the steel is known during various stages of the process. In the present work oxygen activities have been measured in liquid iron, manganese, and iron alloys with galvanic cells using ZrOz(CaO) and s solid electrolytes with the object of establishing the range of oxygen pressure in which these materials can be used as electrolytes at steelmaking temperatures. Calcia-stabilized zirconia and Tho2-Y203 solid solutions are oxygen ion conductors. Such electrolytes were first used by Kiukkola and Wagner1 and Peters and ~ann&apos; in galvanic cells for the determination of thermodynamicquantities of oxide systems in the temperature range 700" to 1200°C. At these moderate temperatures calcia-stabilized zirconia has been found to exhibit predominantly ionic conductivity at oxygen pressures as low as those for the Cr + Crz03 equilibrium,394 but at lower oxygen pressures elec- tronic contribution to conductivity becomes significants4 The Th02-Y203 solid solutions are ionic conductors at oxygen pressures lower than those applicable to zirconia base electrolytes.5&apos;6 At high oxygen pressures Thoz base electrolytes exhibit significant p-type semiconduction. At the time the present experiments were carried out several papers1&apos;-* were published on the electrochemical determination of oxygen activities in liquid iron using the ZrOz(CaO) electrolyte. The results of different authors do not agree well. For instance, according to Fischer and ~ckermann" stabilized zirconia can be used to measure oxygen contents in liquid iron larger than 0.02 wt pct, but according to Baker and west1&apos; ZrOz(CaO) cannot be used for the determination of oxygen content in liquid iron because of high electronic contribution to the conductivity. Fig. 1 is a schematic diagram of the apparatus used. About 500 g of liquid metal is contained in a crucible into which a stabilized zirconia or Th02(Y203) tube is immersed. A platinum contact wire is pressed (with a spring mechanism) against the inside bottom wall of the electrolyte tube. The tube is flushed continuously with a stream of air, CO-CO, (or Hz-C02) (at 0.96 atm and at a rate of about 300 cu cm per min), via an alumina tube inserted inside the electrolyte tube. This alumina tube also contains the Pt-Pt/10 pct Rh thermocouple. A capillary alumina tube shielding the other contact wire is immersed in the melt. The molybdenum contact wires were used mostly; in some cases platinum wire was employed. Molybdenum has the advantage that it dissolves more slowly in the melt than platinum. The whole cell was contained in the alumina reaction tube of a resistance furnace with molybdenum winding. The reaction tube was closed gas tight at both ends and flushed continuously with argon. Because of the poor thermal shock resistance of the electrolyte tubes the cell had to be assembled in the cold furnace. The electrolyte tube and alumina sheath

Jan 1, 1968

By F. S. Pettit

The oxidation of Ni-3 to 25 wt pd Al alloys has been studied in 0. 1 atm of oxygen at temperatures between 900° and 1300°C. These alloys have been found to oxidize by three different mechanisms which depend on the temperature of- oxidation and the alloy composition. Two of the three mechanisms do not permit a continuous layer of Al,0, to be formed on the alloy surface and the oxidation rates are greater than that for pure nickel. The third mechanism results in the formation of an external A1203 scale and lke oxidation rates are about three orders of magnitude smaller than those for pure nickel. The minimum amount of aluminum required for the formation of external scales of A L,0, has been determined. NICKEL-base alloys are currently the main source of materials for use at elevated temperatures in gas turbine engines. These alloys are usually coated to obtain oxidation resistance. Coatings on nickel-base alloys are frequently formed by reaction of the alloy with aluminum whereby alloyed nickel aluminides are formed. The alloyed nickel aluminides provide protection to the nickel base alloy because external scales of A1203 (alumina) are formed during oxidation and mass transport through A120, is slow in comparison to mass transport through most other oxides. In view of the protective properties of A1203, it is important to know how much aluminum is required in these alloys in order to form external scales of AlzO,. The present paper is concerned with the oxidation kinetics and the oxidation mechanisms of Ni-A1 alloys and the minimum amount of aluminum required in these alloys for the formation of external scales of Alz03. THEORETICAL CONSIDERATIONS When a Ni-A1 alloy is heated in oxygen at elevated temperatures, the following reactions can take place on the surface of the alloy where the oxide phases are assumed to be virtually pure: These oxide phases are in the form of nuclei scattered over the surface of the alloy and, in view of their rapid formation, they need not be in equilibrium with the alloy. As the oxidation process continues, equilibrium between the alloy surface and the oxide phases is approached and the stability of the oxide nuclei is determined by the composition of the alloy at the alloy/oxide interface because of the following reactions: 3NiA1204 + 2A1 (alloy) = 4AlzO3 + 3Ni (alloy) [41 4Ni0 + 2Al (alloy) = NiA120, + 3Ni (alloy) [ 5 1 Application of the mass-action law to Eqs. [4J and [5J yields the following equilibrium conditions for these reactions: where aA1 and aNi are the activities of aluminum and nickel, are the standard free energies of formation of NiO, A1203, and NA1204, respectively, R is the gas constant, and T is the absolute temperature. If the composition of the alloy at the alloy/oxide interface is such that (akl/ahi) is greater than the equilibrium values defined by Eqs. [6] and [7], then Reactions (41 and [5] will go to the right as written. Conversely, if the alloy composition is such that the activity ratio (aLl,/aki) at the alloy/oxide interface is less than the equilibrium values, then Reactions [4] and [5] will proceed to the left. The equilibrium activity ratios in Eqs. [6] and 171 can be calculated since values for the standard free energies of formation of the oxide phases are available. Standard free energies of formation for NiO and A1203 have been tabulated by Elliott and ~leiser.&apos; The standard free energy of formation for NiA1204 can be obtained from the data of Tretjakow and Schmalzried.&apos; The results of these calculations are tabulated in Table I. Table I shows that the following inequality is valid over the temperature interval 900" to 1300°C: (Reaction [5]) (Reaction [4]) « 1and therefore the aluminum activity for these compositions can be taken as equal to the square root of the activity ratios (i.e., aNi = 1). If equilibrium is estab-

Jan 1, 1968

By E. P. Sadowski, L. P. Trudeau, C. R. Cupp

The apparent high radiation resistance of two varieties of maraging steel is described and an indication is given of some phenomena that require further study. Two aspects were included in this work: a) effects of neutron irradiation on the room-ternperature tensile properties of 18 Ni (250) maraging steel; b) effects of neutron irradiation on the room-temperature tensile properties and on the impact resistance of 12 pct Ni-5pct Cr-3 pct Mo maraging steel. Subsize tensile and impact test specimens were used. The 18 pct Ni steel was irradiated to a neutron fluence of 3.3 x 10 n per sq cm (>1 mev). The 12-5-3 variety was irradiated to two neutron fluence levels: 1) 1.5 x 10 per sq CTTL (>I mev) 2) 3.1 x 10&apos;9nper sq cm (>1 mev) In all respects both varieties showed unusually high resistance to change in strength and ductility after neutron irradiation. There was no noteuorthy over-aging in fully aged specimens. The aged 18 pct Ni variety showed a 4 pct drop in yield strength upon irradiation with little or no decrease in ductility. The aged 12-5-3 variety showed a 5 pct increase in yield strength on irradiation with a very slight decrease in ductility. The impact transition of the 12-5-3 variety only increased 35 to 45 Co upon irradiation, and the shear energy fracture value for the subsized specimens decreased only half as much as expected frorn experience with conventional steels. THE development of new reactor concepts and nuclear technology now depends to a large extent on the availability of new alloys capable of operating in stringent reactor environments. One of the most important new types of metallurgical material that has been developed in recent years is the maraging steels. This type of alloy is notable for its remarkable retention of toughness at high strength levels. In the course of a research program which incorporated ambient temperature radiation effects studies to determine the mechanisms of strengthening of 18 pct nickel maraging steel,&apos; it became evident that the resistance of the alloy to neutron-induced changes in mechanical properties should be studied. This paper is to present evidence for the apparent high radiation resistance of maraging steel. The experimental program was in two parts: a) Effect of neutron irradiation on the room-temperature tensile properties of 18 Ni (250) maraging steel. b) Effect of neutron irradiation on the room-temperature tensile properties and on the impact resistance of 12 pct Ni-5 pct Cr-3 pct Mo maraging steel, a cobalt-free alloy. EXPERIMENTAL PROCEDURE 18 Ni (250) Maraging Steel. Tensile test specimens were machined to the dimensions shown in Fig. 1 from $-in.-diam hot-rolled bar of the composition shown in Table I. All specimens were austenitized for 1 hr at 1500°F (815°C) in argon and water-quenched. Half of the specimens were then mar aged for 3 hr at 900° F (482°C) in argon. The specimens were irradiated in a fast neutron transformer rod at approximately 120°F (50°C) to a neutron fluence of 3.3 x 10 10 n per sq cm (>1 mev). The irradiation was performed in the NRX reactor of Atomic Energy of Canada, Ltd., at Chalk River, Ontario, Canada. In all cases, the thermal neutron flux was three times as high as the reported (> 1 mev) fluxes. The room-temperature tensile tests were performed with an Instron tensile testing machine operating at a crosshead speed of 0.05 in. per min. The loading frame of the machine, mounted in a hot cell, was remotely controlled. The specimens were tested either

Jan 1, 1968

By G. S. Cole

The temperature has been measured ahead of stationary solid-liquid interfaces under conditions approximating luzidirectional heat flow and therefore unidirectional solidification. Natural convection flow patterns may be deduced from the temperature distributions , temperature fluctuations, and shape of the interface. Fluid flow increases with the height and the rate of heat transfev through the interface and this is further manifested by a deviation of the interface from aflat vertical plane. The influence of fluid flow on solute inhomogeneity during alloy crystal growth can be inferred from the observed temperature distributions. A buoyancy force exists in the liquid ahead of a vertical solid-liquid interface, caused by a difference in density between cold fluid near the interface and warmer fluid in the bulk liquid. When the viscous and inertia forces in the melt exceed this buoyancy force, a flow of fluid takes place, termed natural or free thermal convection. Natural convection in purely liquid systems has been extensively studied for many years. 1"u On the other hand, fluid flow during horizontal crystal growth has oniy recently been the subject of experimental investigation."-25 The requirements for horizontal crystal growth differ from other heat flow systems. The small aspect ratio (ratio of height of cold wall to length of fluid) has never been considered. The uniform furnace gradient which supplies heat radially (and not necessarily symmetrically) differs from previous boundary conditions of uniform heat flux at the cold and hot ends. And most important of all an isothermal s/l interface is present which can adjust its shape and position to conform to heat and fluid flow. All of these boundary conditions involve complexities which cannot be readily solved analytically. Preliminary observation has demonstrated the penera1 shape of the natural convective flow pattern in transparent media.20&apos;24&apos;25 The flow is circulatory, directed toward the interface at the surface of the liquid, down and away from the interface at the bottom, and then up at the hot end of the melt. During crystal growth such a flow may interact with the solute boundary layer at the s/l interface to affect solute incorporation.M&apos;1B|28&apos;i!T Evidence has also been presented recently to show that thermal convective flow will affect the structure of ca~tin~s.~~-~~ The rate of heat transfer (conduction plus convection) in a given fluid system is a function of the temperature difference between the hot end of the liquid and the s/l interface and the height of the interface. At the lowest values of these variables* all heat is *It has been shown&apos; that adverse temperature gradients as low as O.OOS°C oer cm are sufficient to cause convection. transferred by conduction. When the temperature difference or interface height are increased, laminar fluid flow commences and heat transport takes place by laminar convection as well as by conduction; turbulent heat transfer takes place at higher values of these variables. In the transition region between laminar and turbulent flow, boundary layer separation takes place; fluctuations in temperature are also noted and increase in amplitude and frequency as turbulence becomes dominant. In this paper, fluid flow patterns in the melt ahead of a stationary interface are deduced from observations of temperature distribution and fluctuations, heat flow rate, and interface shape. The fluid flow ahead of advancing interfaces and the effect of such flow on solute incorporation may be inferred from these measurements on stationary interfaces. Observations during enforced fluid motion will also be considered. EXPERIMENTAL PROCEDURE The metal was contained in a lava boat 10 cm in length, 1+ cm in width, and 2 cm in height, as shown in Fig. 1. A water-cooled, molybdenum block heat-sink is at one end of the boat; surrounding this assembly is a slotted stainless-steel tube noninductively wound with a nichrome heating element. Temperature was measured by 38-gage Chrome1 vs Alumel thermocouples sheathed in 0.05-cm-diam graphite-coated stainless-steel tubing, which were moved longitudinally and vertically through the melt by means of a two-dimensional motorized micrometer stage. In some experiments the thermocouple junction was exposed, but in the majority of experiments the junction was welded to the sheath tip; no significant difference

Jan 1, 1968

By G. R. Purdy, J. A. Malcolm

The isothermal dendritic precipitation of y in p CuZnSn is compared with the isothermal formation of Widmanstatten a plates in p CuZn. Although both precipitates are evidently bounded by semicoherent interfaces, the dendritic shape of y evolves through smooth "sinuoidal" shape perturbations, while a-p interfaces tend to be strictly planar, or rnicroscopically faceted. An estimate of the average inter-facial free energy of cube-oriented y in p through the Mullins-Sekerka analysis indicates that it is low (of the order of 50 ergs per sq cm). Interface mication is apparently controlled by volunle dij&apos;usion, and the observed anisotropy in growth probably results from anisotropy of inter facial free energy. Studies of the grain boundary precipitation of y in p indicate that the precipitate can grow in both $ grains, but becomes unstable with respect to the grain with which it shares a mobile semicoherent interface. Facets observed at the tips of Kurdjumov-Sacks-oriented Wid-manstatten a plates correspond to variants of an irrational hahit, near (231)0. Comparison with Hu and Smith&apos;s determination of relative interfacial free energies of a-(3 boundaries suggests that this system possesses an extremely deep o cup, which results in an ej&apos;ective low-o zone. The possible effects of such a cup on the stability of a-p interfaces are discussed, a needles, grown during rapid continuous cooling, possess microscopically smooth interfaces, and are characterized by a high degree of&apos; damage in the region of the boundaries. These boundaries, induced to move on tempering at 200"C, become faceted as equilibrium is approached, which seems to indicate that boundary structure and mobility in this system are dependent on the local degvee of departure from equilibrium MULLINS and sekerkal have elucidated the phase boundary stabilizing effect of surface tension. a factor not taken into account in previous treatments of morphological development. Their analysis applies to the isothermal growth of a pure spherical precipitate (planar in the limit of infinite radius) in a slightly supersaturated solution, under conditions of inter-facial local equilibrium and isotropy of interfacial free energy. More recently, several other factors which might tend to stabilize planar interfaces have received attention. These are: i) interface diffusion;4"8 and ii) slow interfacial reaction. cahn7 included a slight anisotropy in interfacial free energy, and showed that it has no stabilizing effect, but forces shape perturbations to reflect the anisotropy. shewmon4 noted that dendritic morphologies are rarely observed in solid-solid systems, and, in particular, postulated that slow interfacial reaction occurs at all boundaries between proeutectoid ferrite and austenite, except those which propagate parallel to {11 l)y planes (for Kurdjumov-Sachs [K-S] related phases). Previously, Aaronson~ had proposed interfacial reaction at the broad faces of Widmanstatten plates, and expected that the lateral motion of high-mobility incoherent ledge edges would produce planar precipitates bounded by law-mobility semi-coherent interfaces. The problem of interfacial reaction during the dif-fusional formation of precipitates has often been ignored, although it is apparent that a small component of chemical reaction must exist at any moving interface." Further, all solutions of the diffusion equations for boundary conditions corresponding to isothermal growth predict infinite growth rate at time zero, so that elements of interfacial reaction would be most easily detected at early times. However, reported deviations from diffusion control are comparatively rare," and the local-equilibrium diffusion-control model appears adequate for the description of many isothermal growth systems.&apos;2"9 Cahn14 has treated the problem of migration of an interface which is able to reach positional energy minima, and concluded that such an interface, if subjected to a high local ther-modynamic "driving force", may migrate normal to itself without the benefit of ledges. As local equi-

Jan 1, 1968

By Emerson F. Heald

A systematic study was made of new and old data on chemical activities in Fe-Pt alloys at elevated ternperatuves. Experimental results may be expressed in terms of the excess free energy using Least-squares analysis of the data gave the following values for the constants: for the temperature range 1130° to 1350°C, and tentatively to 155O°C, B = -3.326564 and C = 0.221051; for the temperature range 650" to 850°C, B = -2.555690, C = 1.762735, and D =0.097196. In the study of iron-containing silicate systems, it is sometimes desirable to have a direct experimental measure of the activity of iron in the system. The well-known solubility of iron in platinum, often a headache in experimental work on iron compounds under reducing conditions, can be used to advantage in this respect. If the activity of iron in an Fe-Pt alloy in equilibrium with the silicate is known as a function of the composition of the alloy, chemical analysis of the alloy will give a knowledge of the activity of iron in all of the phases in the system. The present study was undertaken in order to elucidate the characteristics of Fe-Pt alloys as iron activity indicators. This work is intended to tie together some previous work, which may be summarized as follows. Larson and Chipman1 determined the activity of iron in Fe-Pt alloys at 1550°C by equilibrating platinum metal with calcium oxide-iron oxide-silica melts of known iron activity. Compositions of the resulting alloys were determined by chemical analysis. A similar study was carried out by Taylor and ~uan,&apos; who worked at 1300°C. They brought the Fe-Pt alloys into equilibrium with iron oxide under conditions of known partial pressure of oxygen, and thus, from the work of Darken and ~urr~,~ conditions of known iron activity. Compositions were determined indirectly, by following the change in weight of the sample. Sundaresen et el* used the electromotive force of cells in which the alloy formed one electrode in order to measure the activity of iron in the alloy at 650" and 850°C. These temperatures were chosen to be above and below the first-order phase transition which takes place upon the ordering of Fe3Pt and the second-order transition which occurs upon the ordering of FePt3. EXPERIMENTAL 1) High Temperatures. The starting materials used were thin platinum foil, about 0.002 mm thick, and Fisher Certified reagent ferric oxide, Fez03, which had been heated for 24 hr at 1000°C. An intimate mixture of 80-mesh Fez03 and platinum platelets was placed in a thin platinum foil envelope. The latter was suspended from thin platinum wires in the hot zone of a vertical-tube, platinum-wound furnace of the type described by Muan and ~sborn.~ A capillary gas mixer similar to that used by Darken and Gurry3 was used to prepare a precisely known mixture of carbon dioxide and hydrogen, which was allowed to flow upward through the furnace tube. The partial pressure of oxygen in contact with the sample was thereby fixed at a value which was calculated from the charts prepared by porter? Temperatures were measured with a Pt-10 pct Rh-in-platinum thermocouple, which was calibrated using the melting points of gold (1062 .@C) and diopside, CaMgSizOB (1391.5"C). Temperature control was maintained to within i3"C with a Geophysical Laboratory proportional controller, using the furnace resistance as the sensing element. Samples were quenched by passing a small current through the platinum suspension wires, allowing the sample to drop into a bath of dibutyl phthalate at the bottom of the furnace tube. Prior to chemical analysis the samples were washed with acetone and dried. 2) Chemical Analysis. It proved possible, in almost all cases, to separate the Pt-Fe platelets physically from particles of iron oxide. The platelets were dissolved in a small volume of aqua regia, evaporated to dryness, and redissolved to 0.1 M HC1. In order to determine iron in the platinum alloy potentiometrically, it is necessary first to remove the platinum. A 10-cm column of Amberlite IR-120 cation exchange resin in the hydrogen form provided separation quickly and quantitatively: The mixture of iron and platinum in 0.1 M HC1 was added to the top of the column, and washed with about 100 ml of 0.1 M HC1. Under these conditions, the iron, principally in the form of cations such as FeC1" and FeCl;, is held quantitatively in the uppermost centimeter of the column. The platinum, in the form of anions such as PtC&- , is washed through without being adsorbed. After a qualitative test with stannous chloride indicated all of the platinum was removed, the iron was

Jan 1, 1968

By K. Mukherjee

A quasi-thermodynamic calculation is presented for estirt~ating vacancy Parameters in fcc metals. For fcc metals the equilibrium vacancy concentration at the melting point can be approximated by a constant mole fraction. The Gibbs free energy of formation of the vacancies can then be expressed as a simple function of the absolute melting temperature alone. From this description the formation energy Ef, the vibrational entropy Sv, and the formation volume of a vacancy can be calculated in terms of known thermodynamic parameters. The calculated values are in good agree-rnent with available experimental results. IT appears that many of the physical parameters associated with lattice defects can be empirically related to thermodynamic melting parameters.&apos;-7 Besides the implicit correlations between melting phenomenon and point defects, the melting temperature itself at atmospheric pressure can be used as a reference temperature for the purpose of comparison of vacancy concentrations in a given crystal class. The concentration at the melting point then corresponds to the maximum vacancy super saturation in the crystalline state at a fixed pressure. For pure fcc metals such as Au, Cu, Al, Ag, Pb, and Pt the mole fraction of vacancies at the melting point8 is of the order of 10*"3 to 10"1. The equation expressing the equilibrium vacancy concentration at the melting point contains three parameters: the formation energy, the vibrational entropy, and the absolute melting temperature, see Eq. [2]. Since these three parameters cover a wide range of values8 in the above-mentioned metals, it can be assumed that in other fcc metals, for which no reliable data are available, the mole fraction of vacancies at the melting point most likely lies in the range 10~3 to lO"4. This is then the basis of the calculations described in this article. Within this range the mixing entropy can be linearized and the vibrational entropy, the formation energy, and the vacancy formation volume can be calculated in terms of known thermodynamic constants. 1} LINEARIZATION OF MIXING ENTROPY The Helmholtz free energy of a crystal containing n vacancies at the melting point can be writteng as where Ef, T,, k, and S, are the formation energy of a vacancy, the absolute melting temperature, Boltz-mann&apos;s constant, and the vacancy formation entropy, respectively. After applying Stirling&apos;s approximation in Eq. [l] and minimizing with respect to n where (n/N), is the equilibrium vacancy concentration in mole fraction at the melting temperature at 1 atm pressure. If instead of setting (6~/6n) = 0 immediately after Stirling&apos;s approximation in Eq. [I], the configurational partition function is simplified, then some useful and significant results can be obtained by utilizing the experimental inforrnation After applying Stirling&apos;s approximation and rearranging is plotted as a function of (n/N) in Fig. 1. The points, not all of which are shown, are fitted by a straight line substituting from Eq. [5] into Eq. [I] and minimizing with respect to n combining Eqs. [6] and [2] It must be emphasized that Eq. [7] is only a crude approximation based on an oversimplified model of

Jan 1, 1967

By C. Y. Cheng

THE purpose of this note is to show that the dislocation mechanism controlling the creep of Fe-4 pet Si alloy1 may equally account for the behavior of a-Fe2 over the same temperature range. A recent study of the creep behavior of a-Fe has been made by Ishida et al.2 Their results were in agreement with the mechanism of nonconservative motion of jogged screw dislocations over the entire range of temperatures investigated, from 480° to 1045°K. However, the observed creep rate was much higher than that which could be accounted for by the above model unless the authors assumed that pipe diffusion became significant below 775°K. More recently, Cheng et al.1 inves-gated the creep of Fe-4 pet Si alloy over about the same temperature range and found that the results could be correlated fairly well with a dislocation climb mechanism as represented by Eq. [l]. Proceeding as shown previously,1 if creep is controlled by a single climb mechanism, at intermediate stresses, the shear creep rate, y, can be represented by where n and K are material constants {K is independent of the temperature but dependent on the structure, that is, K decreases during the primary stage and reaches a steady-state value over the secondary stage of creep), t is the applied shear stress, G is the shear modulus, gc is the free energy of activation for creep (usually equal to that for self-diffusion, gd), and RT has the usual meaning. By solving for y, the apparent activation energy for creep, Q which can be determined experimentally, is given by where hc is the enthalpy of activation for creep which usually is also equal to that for self-diffusion, h^. By using Eq. [2], the data in Fig. 2 of Ref. 2 can be re-plotted as shown in Fig. 1. By comparing the two figures, it is seen that the slight increase in the apparent activation for creep over Region II, as noted in Fig. 2 of Ref. 2, is due to the influence of temperature on the shear modulus rather than of the stress on the

Jan 1, 1969

By Richard J. Fruehan

ThE thermodynamic activities of nickel and chromium in liquid Ni-Cr alloys have not been previously reported. There have been several investigations on the solid alloys.1-3 In the present investigation the activity of chromium in liquid Ni-Cr alloys at 1600° C was determined by the use of the following galvanic cell, The use of galvanic cells employing solid oxide electrolytes for determining the activity of metals in solid alloys was first demonstrated by Rapp and Maak4 on Cu-Ni alloys between 700° and 1000°C. Recently Schwerdtfeger5 tested the performance of the ZrO2(CaO) electrolyte at 1600°C and found it satisfactory for oxygen pressures as low as 10"12 atm. He also demonstrated the use of solid oxide electrolytes for determining the activities in liquid metal systems in measuring the activity of manganese in Fe-Mn alloys at 1500°C. Extensive investigations have been carried out in this laboratory, exploring the oxygen partial pressure lower limit at which ZrO2(CaO) electrolyte can be used satisfactorily in oxygen galvanic cells at 1600°C. In a paper to be published at a later date,9 it is demonstrated conclusively that ZrO2(CaO) exhibits insignificant electronic conductivity at oxygen pressures down to about 3 x 10"13 atm which is lower than the oxygen partial pressure in equilibrium with Cr-Cr2O3 at 1600°C. Therefore, the activity of chromium can be related to the measured reversible electromotive force of the cell in the present investigation since no electronic short circulating will occur. Fig. 1 is a schematic diagram of the cell used. The Cr-Cr2O3 electrode was made of equal weights of chromium and Cr2O3 powders which were mixed and packed into a recrystallized alumina crucible. A Pt-wire lead was embedded into the Cr-Cr2O3 compact to insure good contact. A ZrO2(CaO) crucible, supplied by the Zirconium Corp. of America, contained the Ni-Cr melt equilibrated with solid Cr2O3. The ZrO2(CaO) crucible was placed on the Cr-Cr2O3 electrode and additional Cr-Cr2O3 mixture was packed around it. Contact with the Ni-Cr alloy was made with a Cr2O3 tube, which is a weak electronic conductor. A platinum wire lead was attached to the Cr2O3 tube. The galvanic cell was lowered slowly into the hot zone of the furnace tube in order to avoid too large a thermal shock which could break the ZrO2 (CaO) crucible. The furnace was con- tinuously flushed with purified argon during the experiment. The temperature was measured with a Pt-Pt/10 pet Rh thermocouple and maintained at 1600° ± 5°C. The electromotive force was measured with a recording potentiometer. The furnace was turned off when measurements were being made in order to avoid induction effects and the reversibility of the cell was demonstrated in the usual manner. The electromotive force was measured several times over a period of approximately 1 hr. During that period the electromotive force remained constant within ± 3 pet and did not continuously drift in any one direction. After the experiment the alloys were analyzed for chromium in the usual manner. The measured electromotive forces of the cell at 1600°C, (2912°F), are listed in Table I. The activity of chromium, with solid pure chromium as the reference state, (a), was calculated using Eq. [l], , n F E I, n lna RT- U] where E is the measured electromotive force, F is the Faraday constant, and n is equal to 3, the number of equivalents per mole, (nF/RT = 18.59 volts&apos;1 at 1600°C). The resulting activities are listed in Table I. The activity of chromium relative to pure liquid chromium was also calculated. The free energy of fusion of chromium at 1600° C was calculated using

Jan 1, 1969

By J. H. Swisher

The solubility of graphite in CaO-S2O2-Al,O3 slags was measured by equilibrating slag samples with graphite crucibles and CO gas. Carbon contents as high as 2 ut pct were obtained in CaO-saturated, CaO-A1,O3 slags, and 1.3 wt pct in slags of the composition CaO.Si0,. Although the observed conditions for Sic formation were in agreement with those predicted from thermodynamic data, CaC, was found to form at a lower temperature than predicted frotn thermodynamic data. From measurements of the equilibrium carbon content as a function of CO Partial pressure, it was found that carbide ions dissolve in CaO-A12O3 melts with a valence of minus two. The carbon content increased with CaO concentration in Ca0-Al,O3 melts and increased with SiO, content along the CaO&apos;AlO3-CaOSi0 join in the ternary system. When solid CaC2 was added to CaO-A12O3 and CaO-SiO2-A12O3 slags, it was found that one of the oxides in the slag was reduced by the carbide (Al2O3 in the forrner and SiOz in the latter). In electric furnace steelmaking, a double-slag practice is frequently used to meet alloy specifications. Initially a flush slag, which is oxidizing in nature, is used to remove phosphorus and carbon from the steel bath. Later in the refining period, the flush slag is replaced by a highly reducing carbidic slag. When calcium carbide is formed in or added to a finishing slag, the slag is effective as a desulfurizing agent and also permits alloying elements such as chromium, vanadium, and tungsten to be added to the slag in the form of oxides. The oxides are readily reduced by calcium carbide, thereby minimizing the use of expensive ferroalloys. More work has been done on the thermodynamics of silicon carbide in slags than on calcium carbide. Baird and alor&apos; and Kay and alor&apos; determined the free energy of formation of Sic by measuring the partial pressure of CO in equilibrium with solid silica, silicon carbide, and graphite. Using a similar technique, they determined SiOz activities in CaO-SiOz and Ca0-Si0,-A1203 slags. Rein and chipman3 also determined the free energy of formation of Sic using slag-metal equilibrium measurements. A literature survey has uncovered only one experimental study of the behavior of CaC, in slag systems. Shanahan and cooke4 report the results of some preliminary experiments on the solubility and stability of CaC, in a CaO-A1,03 and a Ca0-Si0-A1,03 slag at a temperature of about 1500". The carbon solubility as CaC, in a slag containing 50 pct CaO and 50 pct A1203 was reported to be 0.6 pct. They also review earlier work on the binary CaO-CaC, system. A eutectic exists in this system, but various investigators disagree on the eutectic temperature and composition. eal has given an explanation for carbide furnace erruptions in terms of the thermodynamic properties of CaC,; his analysis is not based on experimental data, but on compiled data for the free energies of formation of CaC, and CO.&apos; , These data for steel-making temperatures are all extrapolated from the results of low-temperature measurements. In the experiments described in this paper, slag samples were equilibrated with graphite crucibles and with mixtures of CO and argon or with CO gas at 1 atm total pressure for measurement of the carbon solubility. Most of the work was done on Ca0-A1203 binary slags, although in some experiments CaO-SiO, and Ca0-Si0,-A1,03 slags were used. EXPERIMENTAL Slag samples of the desired composition for the solubility measurements were obtained by blending pre-fused master slags. The master slags were prepared by fusing mixtures of reagent-grade CaC03 with either A1,03 or Si0, in a graphite crucible. The master slags were crushed, then decarburized in air in a muffle furnace at 1200O C. A schematic diagram of the apparatus is shown in Fig. 1. The source of carbon for the solubility meas-

Jan 1, 1969